The present invention is directed to golf balls. More particularly, the present invention is directed to a novel dimple packing method and novel dimple patterns. Still more particularly, the present invention is directed to a novel method of packing dimples using phyllotaxis and novel dimple patterns based on phyllotactic patterns.
Dimples are used on golf balls to control and improve the flight of the golf ball. The United States Golf Association (U.S.G.A.) requires that golf balls have aerodynamic symmetry. Aerodynamic symmetry allows the ball to fly with little variation no matter how the golf ball is placed on the tee or ground. Preferably, dimples cover the maximum surface area of the golf ball without detrimentally affecting the aerodynamic symmetry of the golf ball.
Most successful dimple patterns are based in general on three of five existing Platonic Solids: Icosahedron, Dodecahedron or Octahedron. Because the number of symmetric solid plane systems is limited, it is difficult to devise new symmetric patterns.
There are numerous prior art golf balls with different types of dimples or surface textures. The surface textures or dimples of these balls and the patterns in which they are arranged are usually defined by Euclidean geometry.
For example, U.S. Pat. No. 4,960,283 to Gobush discloses a golf ball with multiple dimples having dimensions defined by Euclidean geometry. The perimeters of the dimples disclosed in this reference are defined by Euclidean geometric shapes including circles, equilateral triangles, isosceles triangles, and scalene triangles. The cross-sectional shapes of the dimples are also Euclidean geometric shapes such as partial spheres.
U.S. Pat. No. 5,842,937 to Dalton et al. discloses a golf ball having a surface texture defined by fractal geometry and golf balls having indents whose orientation is defined by fractal geometry. The indents are of varying depths and may be bordered by other indents or smooth portions of the golf ball surface. The surface textures are defined by a variety of fractals including two-dimensional or three-dimensional fractal shapes and objects in both complete or partial forms.
As discussed in Mandelbrot""s treatise The Fractal Geometry of Nature, many forms in nature are so irregular and fragmented that Euclidean geometry is not adequate to represent them. In his treatise, Mandelbrot identified a family of shapes, which described the irregular and fragmented shapes in nature, and called them fractals. A fractal is defined by its topological dimension DT and its Hausdorf dimension D. DT is always an integer, D need not be an integer, and Dxe2x89xa7DT. (See p. 15 of Mandelbrot""s The Fractal Geometry of Nature). Fractals may be represented by two-dimensional shapes and three-dimensional objects. In addition, fractals possess self-similarity in that they have the same shapes or structures on both small and large scales. U.S. Pat. No. 5,842,937 uses fractal geometry to define the surface texture of golf balls.
Phyllotaxis is a manner of generating symmetrical patterns or arrangements. Phyllotaxis is defined as the study of the symmetrical pattern and arrangement of leaves, branches, seeds, and pedals of plants. See Phyllotaxis A Systemic Study in Plant Morphogenesis by Peter V. Jean, p. 11-12. These symmetric, spiral-shaped patterns are known as phyllotactic patterns. Id. at 11. Several species of plants such as the seeds of sunflowers, pine cones, and raspberries exhibit this type of pattern. Id. at 14-16.
Some phyllotactic patterns have multiple spirals on the surface of an object called parastichies. The spirals have their origin at the center of the surface and travel outward, other spirals originate to fill in the gaps left by the inner spirals. Frequently, the spiral-patterned arrangements can be viewed as radiating outward in both the clockwise and counterclockwise directions. These type of patterns are said to have visibly opposed parastichy pairs denoted by (m, n) where the number of spirals at a distance from the center of the object radiating in the clockwise direction is m and the number of spirals radiating in the counterclockwise direction is n. The angle between two consecutive spirals at their center C is called the divergence angle d. Id. at 16-22.
The Fibonnaci-type of integer sequences, where every term is a sum of the previous other two terms, appear in several phyllotactic patterns that occur in nature. The parastichy pairs, both m and n, of a pattern increase in number from the center outward by a Fibonacci-type series. Also, the divergence angle d of the pattern can be calculated from the series. Id.
When modeling a phyllotactic pattern such as with sunflower seeds, consideration for the size, placement and orientation of the seeds must be made. Various theories have been proposed to model a wide variety of plants. These theories can be used to create new dimple patterns for golf balls using the science of phyllotaxis.
The present invention provides a method of packing dimples using phyllotaxis and provides a golf ball whose surface textures or dimensions correspond with naturally occurring phenomena such as phyllotaxis to produce enhanced and predictable golf ball flight. The present invention replaces conventional dimples with a surface texture defined by phyllotactic patterns. The present invention may also supplement dimple patterns defined by Euclidean geometry with parts of patterns defined by phyllotaxis.
Models of phyllotactic patterns are used to create new dimple patterns or surface textures. For golf ball dimple patterns, careful consideration is given to the placement and packing of dimples or indents. The placement of dimples on the ball using the phyllotactic pattern are preferably made with respect to a minimum distance criterion so that no two dimples will intersect. This criterion also ensures that the dimples will be packed as closely as possible.